Sorry to see that.
So the BMS did not work!
A 4A charger, No fuse?.. A sensible voltage on the battery charger would be pointless here.
The trouble is, you had a pack at 10.1V. This means one string (3.2V, 130AH) of the 13.3V four is completely dead and unrecoverable. Recharging makes dead cells hot. Seems the BMS does not take temperature into account.
To kill a cell, it gets discharged then driving the stronger cells to force it into a reverse charge. They get mad hot no matter which way the load is applied from there on. This is easy with top balanced cells as the weakest of the string hits zero first, dies and becomes a dummy load while the BMS (always pathetically) attempts to balance the others down creating more heat!
I'm totally of the Jack Rickard school of Li cells and this simply defines exactly everything he's said